The domain of a function is all of the values that $x$ can be under that specific function. In this case, we're asking what values of $x$ allow $\sqrt{\frac{1}{3} x+2}$ to exist.

In order for square roots to exist, the quantity under the square root must be greater than or equal to $0$ , because you can't take the square root of a negative number. Therefore, we can write the following inequality to solve for $x$ :

$\frac{1}{3}x+2\geq 0$

Solving this inequality, we get:

$\frac{1}{3}x+2\geq 0$

$\frac{1}{3}x\geq -2$ (Subtract $2$ from both sides of the inequality to isolate $x$ )

$x\geq -6$ (Multiply both sides of the inequality by $3$ to get rid of $x$ 's coefficient)

Hope this helps!

8 0

2 years ago

Need to know the area of the composite figure.

MariettaO [177]

Answer:

Step-by-step explanation:

you can figure out the area by using two formulas: area of a circle (on each end are two semi circles which when combined, make a circle) and area of a rectangle

Acircle: pi(r^2) = pi(5^2) = 25pi

Arectangle: length*width = 20*10 = 200ft^2

area of composite figure: (25pi ft^2) + 200ft^2

4 0

3 years ago